Without attempting to cover all the philosophical questions posed by modern mathematics, provides a glimpse of a broad vision of the subject. Covering general philosophical perspectives, foundational approaches, the applicability of mathematics, and history, treats selected topics from a variety of perspectives to demonstrate the range of practices in the discipline. Among them are moderate mathematical fictionism, categorical foundations of the protean character of mathematics, the mathematical overdetermination of physics, and Hungarian traditions and the philosophy of non-classical (...) logic. The 21 papers were presented at a meeting of the International Academy of Philosophy of Science, held in Budapest in May 1993. No index. Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)

We exhibit several counterexamples showing that the famous Serrin's symmetry result for semilinear elliptic overdetermined problems may not hold for partially overdetermined problems, that is when both Dirichlet and Neumann boundary conditions are prescribed only on part of the boundary. Our counterexamples enlighten subsequent positive symmetry results obtained by the first two authors for such partially overdetermined systems and justify their assumptions as well.

Wilson [Dialectica 63:525–554, 2009], Moore [Int Stud Philos Sci 26:359–380, 2012], and Massin [Br J Philos Sci 68:805–846, 2017] identify an overdetermination problem arising from the principle of composition in Newtonian physics. I argue that the principle of composition is a red herring: what’s really at issue are contrasting metaphysical views about how to interpret the science. One of these views—that real forces are to be tied to physical interactions like pushes and pulls—is a superior guide to real forces (...) than the alternative, which demands that real forces are tied to “realized” accelerations. Not only is the former view employed in the actual construction of Newtonian models, the latter is both unmotivated and inconsistent with the foundations and testing of the science. (shrink)

In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there (...) was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (shrink)

For the purposes of this monograph, "by a degree" is meant a degree of recursive unsolvability. A degree [script bold]m is said to be minimal if 0 is the unique degree less than [script bold]m. Each of the six chapters of this self-contained monograph is devoted to the proof of an existence theorem for minimal degrees.

Kurt Gdel was the most outstanding logician of the 20th century and a giant in the field. This book is part of a five volume set that makes available all of Gdel's writings. The first three volumes, already published, consist of the papers and essays of Gdel. The final two volumes of the set deal with Gdel's correspondence with his contemporary mathematicians, this fourth volume consists of material from correspondents from A-G.

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Structural realism is sometimes said to undermine the theory underdetermination (TUD) argument against realism, since, in usual TUD scenarios, the supposed underdetermination concerns the object-like theoretical content but not the structural content. The paper explores the possibility of structural TUD by considering some special cases from modern physics, but also questions the validity of the TUD argument itself. The upshot is that cases of structural TUD cannot be excluded, but that TUD is perhaps not such a terribly serious anti-realistic argument.

This essay examines the relation between causation and causal explanation. It distinguishes two prominent roles that causes play within the sciences. On the one hand, causes may work as metaphysical posits. From this standpoint, mainstream in contemporary philosophy, causation provides the ‘raw material’ for explanation. On the other hand, causes may be conceived as explanatory postulates, theoretical hypotheses lacking any substantial ontological commitment. This unduly neglected distinction provides the conceptual resources to revisit longstanding philosophical issues, such as overdetermination and (...) causal pluralism. It also inspires a provocative reframing of Russell’s famous, if notoriously elusive, remarks on the nature of causation. (shrink)

This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate (...) twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson 's "constructible falsity". (shrink)

: Plato’s instructions entail that the line of Republic VI is divided so that the middle two segments are of equal length. Yet I argue that Plato’s elaboration of the significance of this analogy shows he believes that these segments are of unequal length because the domains they represent are not of equally clear mental states, nor perhaps of objects of equal reality. I label this inconsistency between Plato’s instructions and his explanation the “overdetermination problem.” The overdetermination problem (...) has been a perennial concern, and a substantial amount of work has been produced which attempts to deal with it. I offer a classification of approaches to the overdetermination problem as a way of documenting the problem’s significance, and show why these approaches are all inadequate as solutions. My novel resolution of the overdetermination problem rests upon a demonstration that the contradiction is intentional. The later recapitulation of the ratio at 534a reveals that Plato was himself aware that the middle two segments are equal. I argue that this contradiction is a sophisticated device designed to lead the reader of the Republic through the four epistemic stages represented by the line itself. Most significantly, recognition of this mathematical contradiction acts as a goad, spurring independent philosophical reflection just in the way that Plato advocates in the Republic more generally. (shrink)

Until the late 19th century scientists almost always assumed that the world could be described as a rule-based and hence deterministic system or as a set of such systems. The assumption is maintained in many 20th century theories although it has also been doubted because of the breakthrough of statistical theories in thermodynamics (Boltzmann and Gibbs) and other fields, unsolved questions in quantum mechanics as well as several theories forwarded within the social sciences. Until recently it has furthermore been assumed (...) that a rule-based and deterministic system was also predictable if only the rules were known, but this assumption has now been undermined by modern chaos-theory describing rule-based and deterministic, but unpredictable systems, while catastrophe-theory delivers a set of types describing various kinds of instability and conditions for the stability of a given system. Hence the main trait in the theoretical development in the 20th-century science can be described as a basic modification and limitation of some of the fundamental and strong assumptions forwarded in the previous epochs of modern science. Ironically, the very same process has been a process in which the human capacity to intervene in nature has expanded dramatically and mainly with the help of the very same theories, and not least because they allow nature to be described and made manipulable on a lower level and a more fine-grained scale. While the overall theoretical consistency between the various theories has gone, the reach of human intervention in nature has increased based on quite new dimensions whether in the area of physics (e.g.: energy technologies, chemical technologies, nanotechnologies etc.) or biology (ge¬netic manipulation) or in the area of psychology, sociology and culture (artificial simulations of mental processes, new means of communication, implying changes in the social infrastructure and cultural behaviour etc.). While some of these changes and new conditions can be reflected from within the conceptual framework of rule-based systems, albeit more complex than formerly recognized, others seem to give rise to the question of whether there are »systems« and relations between different systems in the world which are not rule-based? For instance, it seems to be obvious that the notion of instability represents a major conceptual break with former theories of rule-based systems, as the stability of the latter is an axiomatically given property implied in the very notion of rule-based systems, while instability can only be the result of external influence which should be explained as the result of another rule-based sy¬stem. While there are no difficulties implied concerning the stability of rule-based systems, the notion of unstable states of a system raises the question of how there can be a system at all if there are no invariant stabilising principles? This is the first question which I will address. And I shall do so by taking two examples of such systems as my point of departure. The first example will be the computer and the second will be ordinary language. In both cases I will argue that the stability of these systems (which are both defined by the existence/presence of human intentions) are provided by the help of - differently organised - redundancy functions which both allow the maintenance of systems in unstable macro-states, suspension of previous rules, underdetermination and overdetermination and generation/emergence/creation of new rules more or less independent of previous rules by the help of optional recursions to the permanently accessible underlying levels as for instance the level of binary representation in computers. Since the notion of redundancy is both controversial as such and often avoided, the concept is discussed (as defined in Claude Shannon's mathematical theory of information and in the semiotic framework of J. J. Greimas) and leading to a more general definition in which the redundancy functions serve to overcome noisy conditions, but at the cost of rule-based stability, determination, and predictability. A second question will be how the notion of rule-generating systems relates to the notion of anticipatory systems and it will be argued that rule-generating systems share some features with an¬ticipatory systems and that the former from a certain viewpoint can be seen as a subclass of the latter, although anticipative features are not necessarily a part of the definition of rule-generating systems. On the other hand, it will be discussed whether anticipatory systems which are not rule-generating systems can exist and it will be argued that the capacity to anticipate is strongly limited if it is not part of a rule-generating system. Therefore, it is concluded that the most powerful anticipatory systems need to be rule-generating systems. (shrink)

This paper assesses the philosophical heritage of Jacob Klein’s thought through an analysis of the key tenets of his Greek Mathematical Thought and theOrigin of Algebra. Threads of Klein’s thought are distinguished and subsequently singled out (phenomenological, epistemological, and anti-ontological; historical, ontological, and critical), and the peculiar way in which Klein’s project brings together ontology and history of mathematics is investigated. Plato’s theoretical logistic and Klein’s understanding thereof are questioned—especially the claim that the Platonic distinction between practical and theoretical (...) logistic is historically neglected because of Plato’s understanding of the manner of being of mathematical objects—in order to advance the claim that Klein ontologically overdetermines the history of mathematics in a manner that ends up limiting some of his most brilliant analyses of the Greek conception of “numbers” and the philosophical meaning of the notion of “multiplicity.”. (shrink)

This paper assesses the philosophical heritage of Jacob Klein’s thought through an analysis of the key tenets of his Greek Mathematical Thought and theOrigin of Algebra. Threads of Klein’s thought are distinguished and subsequently singled out (phenomenological, epistemological, and anti-ontological; historical, ontological, and critical), and the peculiar way in which Klein’s project brings together ontology and history of mathematics is investigated. Plato’s theoretical logistic and Klein’s understanding thereof are questioned—especially the claim that the Platonic distinction between practical and theoretical (...) logistic is historically neglected because of Plato’s understanding of the manner of being of mathematical objects—in order to advance the claim that Klein ontologically overdetermines the history of mathematics in a manner that ends up limiting some of his most brilliant analyses of the Greek conception of “numbers” and the philosophical meaning of the notion of “multiplicity.”. (shrink)

We have two main aims: to construct mathematical models for analysing determinism, causality and supervenience; and then to use these to demonstrate the possibility of constructing an ontic construal of the operation of free will - one requiring both the presentation of genuine alternatives to an agent and their selecting between them in a manner that permits the attribution of responsibility. Determinism is modelled using trans-temporal ontic links between discrete juxtaposed universe states and shown to be distinct from predictability. (...) Causality is defined on a temporal sequence of δ-algebras and quantified using a measure. The measure leads to definitions of causal overdetermination and epiphenomena. Proofs are constructed to demonstrate deterministic universes must carry their properties essentially but not necessarily locally. We argue determinism and causality are separate doctrines. These models and results are marshalled to put the case that a counterfactual construal of ontic choice cannot work. In response we propose ‘immanence’ - a modified form of indeterminism whereby a universe can present choices to its denizens. We prove that beings subsumed within a universe cannot pilot their own actions. We then argue these beings can exercise free will only when selecting between choices inhering within immanent relata. A being is responsible for its selections if and only if it is constituted of a temporally evolving deterministic substructure. Our proposal is novel: it avoids injecting indeterminism into the decision process. Topological models for property supervenience are developed and used to reconstruct standard definitions from the literature. These are then used to demonstrate considerations of supervenience do not affect our arguments. We have demonstrated that a model of the exercise of free will involving both genuine choices and responsibility is possible but can only operate within a non-deterministic universe possessing specific traits. (shrink)

Widespread causal overdetermination is often levied as an objection to nonreductive theories of minds and objects. In response, nonreductive metaphysicians have argued that the type of overdetermination generated by their theories is different from the sorts of coincidental cases involving multiple rock-throwers, and thus not problematic. This paper pushes back. I argue that attention to differences between types of overdetermination discharges very few explanatory burdens, and that overdetermination is a bigger problem for the nonreductive metaphysician than (...) previously thought. (shrink)

The overdetermination problem has long been raised as a challenge to nonreductive physicalism. Nonreductive physicalists have, in various ways, tried to resolve the problem through appeal to counterfactuals. This essay does two things. First, it takes up the question whether counterfactuals can yield an appropriate notion of causal redundancy and argues for a negative answer. Second, it examines how this issue bears on the mental causation debate. In particular, it considers the argument that the overdetermination problem simply does (...) not arise on a dependency conception of causation and shows why this idea, though initially appealing, does not address the real problem. As the essay shows, the idea derives its spurious plausibility from the fact that the dependency conception cannot even make sense of our pretheoretic idea of causal redundancy. The essay concludes by briefly discussing a possible picture of mental causation that suggests itself in light of these results. (shrink)

Analyses of factual causation face perennial problems, including preemption, overdetermination, and omissions. Arguably, the thorniest, are cases of omissive overdetermination, involving two independent omissions, each sufficient for the harm, and neither, independently, making a difference. A famous example is Saunders, where pedestrian was hit by a driver of a rental car who never pressed on the (unbeknownst to the driver) defective (and, negligently, never inspected) brakes. Causal intuitions in such cases are messy, reflected in disagreement about which omission (...) mattered. What these analyses mistakenly take for granted, is that at issue is the 'efficacy' of each omission. I argue, on the contrary, the puzzle of omissive overdetermination favors taking the act/omission distinction seriously. Factual causation, properly understood precludes omissions (i.e. omissions are not causal). Of course, the law also attaches liability to omissions, but this works differently from liability for real causes (e.g. omissions have a duty requirement, they also respond differentially to difference-making considerations). The manner in which liability attaches for omissions differs from that of straightforward causal liability, and is entirely dependent on the underlying causal structure. Attention to that structure (e.g. that the driver's hitting the pedestrian with his car is what actually caused the injury) sheds light on which omissions matter (e.g. driver's failure to press on the brakes) and why (because that failure removes a defense the driver would have to liability for the accident he caused). Other cases, where the parties' connection is entirely omissive (e.g. two physicians fail to detect independently lethal conditions), come out differently (tracking moralized elements). The analysis offered makes better sense of both why omissive determination cases are puzzling and how to resolve them. (shrink)

When two rocks shatter the window at once, what causes the window to shatter? Is the throwing of each individual rock a cause of the window shattering, or are the throwings only causes collectively? This question bears on the analysis of causation, and the metaphysics of macro-causation. I argue that the throwing of each individual rock is a cause of the window shattering, and generally that individual overdeterminers are causes.

This work explains how different theories of causation confront causal overdetermination. Chapters clarify the problem of overdetermination and explore its fundamental aspects. It is argued that a theory of causation can account for our intuitions in overdetermination cases only by accepting that the adequacy of our claims about causation depends on the context in which they are evaluated.The author proposes arguments for causal contextualism and provides insight which is valuable for resolution of the problem. -/- These chapters (...) enable readers to quickly absorb different perspectives on overdetermination and important theories of causation, therefore it is a work that will have a broad appeal. (shrink)

The Exclusion Problem for mental causation suggests that there is a tension between the claim that the mental causes physical effects, and the claim that the mental does not overdetermine its physical effects. In response, Karen Bennett puts forward an extra necessary condition for overdetermination : if one candidate cause were to occur but the other were not to occur, the effect would still occur. She thus denies one of the assumptions of EP, the assumption that if an effect (...) has two sufficient causes, it is overdetermined. If sound, her argument does two things: it solves EP, and it shows how to use counterfactuals in order to make the notion of overdetermination precise. However, the argument is not sound. (shrink)

The exclusion problem is held to show that mental and physical events are identical by claiming that the denial of this identity is incompatible with the causal completeness of physics and the occurrence of mental causation. The problem relies for its motivation on the claim that overdetermination of physical effects by mental and physical causes is objectionable for a variety of reasons. In this paper, I consider four different definitions of? overdetermination? and argue that, on each, overdetermination (...) in all cases of mental causation either does not occur or is unobjectionable, even when mental and physical events are non-identical. I therefore conclude that the exclusion problem cannot be used as a reason to accept that mental and physical events are identical unless some other definition of? overdetermination? is provided. (shrink)

Jaegwon Kim’s influential exclusion argument attempts to demonstrate the inconsistency of nonreductive materialism in the philosophy of mind. Kim’s argument begins by showing that the three main theses of nonreductive materialism, plus two additional considerations, lead to a specific and familiar picture of mental causation. The exclusion argument can succeed only if, as Kim claims, this picture is not one of genuine causal overdetermination. Accordingly, one can resist Kim’s conclusion by denying this claim, maintaining instead that the effects of (...) the mental are always causally overdetermined. I call this strategy the ‘ overdetermination challenge’. One of the main aims of this paper is to show that the overdetermination challenge is the most appropriate response to Kim’s exclusion argument, at least in its latest form. I argue that Kim fails to adequately respond to the overdetermination challenge, thus failing to prevent his opponents from reasonably maintaining that the effects of the mental are always causally overdetermined. Interestingly, this discussion reveals a curious dialectical feature of Kim’s latest response to the overdetermination challenge: if it succeeds, then a new, simpler and more compact version of the exclusion argument is available. While I argue against the consequent of this conditional, thereby also rejecting the antecedent, this dialectical feature should be of interest to philosophers on either side of this debate. (shrink)

Among the arguments that have been proposed for physicalism, the “causal argument” is widely taken to be the most compelling. Justin Tiehen (2015) has raised an interesting objection to this argument that takes the form of a dilemma. Tiehen’s ultimate conclusion is that at best, the causal argument is circular and so its premises cannot provide support for its conclusion, physicalism. The aim of the present paper is to respond to Tiehen’s objection in order to provide a defense of the (...) causal argument. (shrink)

The purpose of this paper is to draw attention to a pattern of development, the significance of which has not been generally recognized. This pattern is characterized by an initial occurrence of what I shall call an overdetermined problem - i.e. a problem with no solution compatible with accepted belief and practice - followed by a resolution of the problem which relies on and exploits a change in what was previously taken as given.

It is widely recognized by proponents of the notion that grounding can be, indeed is, overdetermined. Moreover, it seems safe to suppose that something of a consensus has emerged: grounding is overdetermined and there is nothing about it that we ought to find concerning. Not only is the overdetermination apparently not problematic, metaphysically speaking, but that grounding is overdetermined is not problematic, conceptually speaking, either. From a small sampling of alleged cases, however, no such conclusions can responsibly be drawn. (...) And without an account of when a fact is technically overdetermined, we are unable to reasonably answer questions about the acceptability of that overdetermination either. In this paper, I attempt to understand when a fact is technically metaphysically overdetermined. I argue that such an exploration reveals that nothing as regards the overdetermination of grounding is straightforward, and that the phenomenon is deserving of much more philosophical attention. (shrink)

Radical empiricism is the view that experience is the only source of knowledge. Hence, radical empiricism denies the existence of a priori knowledge. Its most famous proponents are John Stuart Mill and W. V. Quine. Although both reject a priori knowledge, they offer different empiricist accounts of the knowledge alleged by their opponents to be a priori. My primary concern in this paper is not with the cogency of their positive accounts. My focus is their arguments against a priori knowledge. (...) My goal is to establish that although they offer very different arguments against the existence of a priori knowledge, each of their arguments suffers from a common defect. They both fail to appreciate the phenomenon of epistemic overdetermination and its role in the theory of knowledge. (shrink)

The paper argues against systematic overdetermination being an acceptable solution to the problem of mental causation within a Humean counterfactual theory of causation. The truth-makers of the counterfactuals in question include laws of nature, and there are laws that support physical to physical counterfactuals, but no laws in the same sense that support mental to physical counterfactuals.

Compatibilists respond to the problem of causal exclusion for nonreductive physicalism by rejecting the exclusionist’s ban on overdetermination. By the compatibilist’s lights there are two forms of overdetermination, one that’s problematic and another that is entirely benign. Furthermore, multiple causation by “tightly related” causes requires only the benign form of overdetermination. Call this the tight relation strategy for avoiding problematic forms of overdetermination. To justify the tight relation strategy, modal compatibilists appeal to a widely accepted counterfactual (...) test. The argument of this paper is that the counterfactual test fails to legitimize the tight relation strategy as it fails to adequately distinguish between problematic and benign overdetermination. Contrary to modal compatibilists, modal dependence does not suffice for benignity. I conclude by arguing that adequately addressing overdetermination worries requires a much heavier metaphysical burden than modal compatibilists have typically recognized. (shrink)

In trying to establish the view that there are no non-living macrophysical objects, Trenton Merricks has produced an influential argument—the Overdetermination Argument—against the causal efficacy of composite objects. A serious problem for the Overdetermination Argument is the ambiguity in the notion of overdetermination that is being employed, which is due to the fact that Merricks does not provide any theory of causation to support his claims. Once we adopt a plausible theory of causation, viz. interventionism, problems with (...) the Overdetermination will become evident. After laying out the Overdetermination Argument and examining one extant objection to it, I will explicate the relevant aspects of an interventionist theory of causation and provide a characterization of overdetermination that follows from such an account. From this, I will argue that the Causal Principle that undergirds the Overdetermination Argument is false and hence the argument is invalid; and I claim that the only other available characterization of overdetermination would render a key premise in the argument false. Thus, the Overdetermination Argument fails to provide us with any reason to deny the causal efficacy of macrophysical objects, and therefore provides no reason to doubt their existence. (shrink)

Among the arguments that have been proposed for physicalism, the “causal argument” is widely taken to be the most compelling. Justin Tiehen (2015) has raised an interesting objection to this argument that takes the form of a dilemma. Tiehen’s ultimate conclusion is that at best, the causal argument is circular and so its premises cannot provide support for its conclusion, physicalism. The aim of the present paper is to respond to Tiehen’s objection in order to provide a defense of the (...) causal argument. (shrink)

A typical thesis of contemporary materialism holds that mental properties and events supervene on, without being reducible to, physical properties and events. Many philosophers have grown skeptical about the causal efficacy of irreducibly supervenient properties, however, and one of the main reasons is an assumption about causation which Jaegwon Kim calls the causal exclusion principle. I argue here that this principle runs afoul of cases of genuine causal overdetermination.Many would argue that causal overdetermination is impossible anyway, but a (...) careful analysis of these arguments shows them to be misguided. Finally, I examine the reasons given in support of the causal exclusion principle, and I conclude that it is plausible if, and probably only if, a certain view of the nature of causation turns out to be correct. Since that view of causation is unacceptable to nonreductivists on other grounds, however, it turns out that exclusion-based arguments essentially beg the question. (shrink)

This paper aims to show that a counterfactual approach to causation is not sufficient to provide a solution to the causal exclusion problem in the form of systematic overdetermination. Taking into account the truthmakers of causal counterfactuals provides a strong argument in favour of the identity of causes in situations of translevel, causation.

Causal overdetermination occupies an uncomfortable place within all the major theories of causation. A natural solution to the problems it gives rise to would be to resolve overdetermination into preemption or joint causation. However, such a solution would seem to lead to individuate events in a fragile manner. The issue of such modal fragility is addressed and it is argued that events designated as effects are always fragile in a natural way and the putative problems of adopting modal (...) fragility can be resolved. It is also studied whether causal overdetermination could work in a setting where the overdetermining causes occur in different levels of reality. Typically postulated higher-level causes are shown to contradict the definitional features of overdetermination. There is thus no reasonable role for causal overdetermination and the notion should be abandoned. (shrink)

Non-Reductive Physicalism is similar in many ways with, what I will call, Orthodox Theism. This strongly suggests that Non-Reductive Physicalist solutions to the Supervenience Argument can be adapted to offer Orthodox Theistic solutions to the Conservation is Continuous Creation Argument. One particular Non-Reductive Physicalist solution will be examined in detail and then applied in the debate over Occasionalism.

In this paper I discuss a famous argument for physicalism – which some authors indeed regard as the only argument for it – the overdetermination argument. In fact it is an argument that does not establish that all the entities in the world are physical, but that all those events that enter into causal transactions with the physical world are physical. As mental events seem to cause changes in the physical world, the mind is one of those things that (...) fall within the scope of the argument. Here I analyze one response to the overdetermination argument that has acquired some popularity lately, and which consists in saying that what mental events cause are not physical effects. I try to show that recent attempts to develop this response are not successful, but that there may be a coherent way of doing so. I also try to show that there seems to be a philosophical niche in which this way might fit. (shrink)

On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.

Causal overdetermination worries arise in a number of domains, but most notably in the philosophy of mind. ln discussions of such worries, alleged examples of causal overdetermination are uniformly viewed as primajzcie problematic. While all alleged cases of overdetermination might be problematic, I aim to show that they are so for different reasons. Examples of causal overdetermination neatly divide into three varieties, corresponding to the connections between the mechanisms and the properties of the causes. Future debates (...) over overdetermination, and mental causation in particular, should pay heed to this distinction. (shrink)

INTRODUCTION MATHEMATICAL logic differs from the traditional formal logic so markedly in method, and so far surpasses it in power and subtlety, ...

Jaegwon Kim argues that if mental properties are irreducible with respect to physical properties then mental properties are epiphenomenal. I believe this conditional is false and argue that mental properties, along with their physical counterparts, may overdetermine their effects. Kim contends, however, that embracing overdetermination in the mental case, due to supervenience, renders the attribution of overdetermination vacuous. This way of blocking the overdetermination option, however, makes the attribution of mental epiphenomenalism equally vacuous. Furthermore, according to Kim’s (...) own logic, physical properties, and not mental properties, may be in danger of losing their causal relevance. (shrink)

Scott Sturgeon has claimed to undermine the principal argument for Physicalism, in his words, the view that 'actuality is exhausted by physical reality' (Sturgeon 1998, p. 410). In noting that actuality is exhausted by physical reality, the Physicalist is not claiming that all that there is in actuality are those things identified by physics. Rather the thought is that actuality is made up of all the things identified by physics and anything which is a compound of these things. So there (...) are tables as well as their microphysical constituents. The argument that Sturgeon has in his sights is the Overdetermination Argument. In what follows, I shall argue that Sturgeon's criticism of the Overdetermination argument fails. I shall also argue that physicalism can accommodate his claim that causal statements concerning the mental and physical respectively may require diverse patterns of counterfactual activity for their truth. (shrink)

I focus on two arguments, due to Jaegwon Kim and Trenton Merricks, that move from claims about the sufficiency of one class of causes to the reduction or elimination of another class of entity, via claims about overdetermination. I argue that in order to validate their move from sufficiency to reduction or elimination, both Kim and Merricks must assume that there can be no ‘weak overdetermination’; i.e., that no single effect can have numerically distinct but dependently sufficient causes (...) occurring at the same time. One problem for both arguments is that weak overdetermination isn't obviously objectionable. That point has been well made before. But I want here to go further than merely shifting the burden of proof onto the advocates of overdetermination arguments. I want to tease out why they are so convinced that we must resist weak overdetermination and explain why their conviction is misguided. Both Merricks and Kim, I shall argue, ultimately rest their case on the same motivating principle, wh.. (shrink)

The use of multiple means of determination to “triangulate” on the existence and character of a common phenomenon, object, or result has had a long tradition in science but has seldom been a matter of primary focus. As with many traditions, it is traceable to Aristotle, who valued having multiple explanations of a phenomenon, and it may also be involved in his distinction between special objects of sense and common sensibles. It is implicit though not emphasized in the distinction between (...) primary and secondary qualities from Galileo onward. It is arguably one of several conceptions involved in Whewell’s method of the “consilience of inductions” (Laudan 1971) and is to be found in several places in Peirce. (From M. Brewer and B. Collins, eds., (1981); Scientific Inquiry in the Social Sciences (a festschrift for Donald T. Campbell), San Francisco: Jossey-Bass, pp. 123–162.). (shrink)